No, it cannot.
You quoted the relevant text already:
Leap. The Steeder can expend all its movement on its turn to jump up to 90 feet vertically or horizontally, provided that is speed is at least 30 feet.
The rules on dashing (PHB, p. 192) state:
When you take the Dash action, you gain extra movement for the current turn. The increase equals your speed, after applying any modifiers. With a speed of 30 feet, for example, you can move up to 60 feet on your turn if you dash.
Any increase or decrease to your speed changes this additional movement by the same amount. If your speed of 30 feet is reduced to 15 feet, for instance, you can move up to 30 feet this turn if you dash.
When you leap for the first time, you have to use all of your currently available movement which, at this moment, is all the movement you have on your turn.
Now, when you take the Dash action, it creates an issue - you now have movement left, but this movement is still on the same turn as the leap. Hence, you now have retroactively invalidated the first use of the Leap, since that requires you to use all [your] movement on your turn.
How to deal with this issue isn't clear from the rules, so your DM will have to make a ruling. I'd personally rule that the first leap isn't affected and you can now use the movement you gained from the Dash for moving.
What you cannot do with this movement is leaping a second time. Assuming you / the Steeder has a speed of 30 feet, you go through the following process during your turn:
- You have 30/30 movement.
- You use all of the movement on your turn (i.e. 30) to leap.
- You now have 0/30 movement left.
- You use the Dash action.
- You now have 30/60 movement on your turn.
- If you want to leap, you would have to use 60/60 movement (all the movement on your turn), but you only have 30. Therefore, you cannot leap.
Note that all of this is just rules-as-written. If your DM decides that a Dash allows a second leap, that's not too far-fetched, from a logical point of view.
Bear in mind, though, that some features might allow the steeder to use Dash as a bonus action, hence allowing it to jump 3*90 feet, i.e. 270, in one turn.